1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
|
#include <numbers>
using std::numbers::pi;
#include "Base/Vector/RotMatrix.h"
#include "Sample/Lattice/BakeLattice.h"
#include "Sample/Lattice/Lattice3D.h"
#include "Tests/GTestWrapper/google_test.h"
// tests volume of the unit cell
TEST(Lattice, volume)
{
R3 a1(4, 0, 0);
R3 a2(0, 2.1, 0);
R3 a3(0, 0, 1);
Lattice3D l1(a1, a2, a3);
EXPECT_EQ(8.4, l1.unitCellVolume()); // 8.4 is the expected volume for the given lattice vectors
}
// tests whether reciprocal lattice basis vectors have been initialized or not
TEST(Lattice, reciprocal)
{
R3 a1(1, 0, 0);
R3 a2(0, 1, 0);
R3 a3(0, 0, 1);
Lattice3D l1(a1, a2, a3);
R3 b1, b2, b3, m_ra, m_rb, m_rc;
// computing expected reciprocal lattice vectors
R3 a23 = a2.cross(a3);
R3 a31 = a3.cross(a1);
R3 a12 = a1.cross(a2);
m_ra = (2 * pi) / a1.dot(a23) * a23;
m_rb = (2 * pi) / a2.dot(a31) * a31;
m_rc = (2 * pi) / a3.dot(a12) * a12;
l1.reciprocalLatticeBasis(b1, b2, b3);
EXPECT_EQ(m_ra, b1);
EXPECT_EQ(m_rb, b2);
EXPECT_EQ(m_rc, b3);
}
// tests whether Lattice has been rotated correctly
TEST(Lattice, transform)
{
R3 a1(1, 0, 0);
R3 a2(0, 1, 0);
R3 a3(0, 0, 1);
Lattice3D l1(a1, a2, a3);
// use rotation by 90 degrees around z axis as a transformation
RotMatrix tr = RotMatrix::AroundZ((2 * pi) / 4);
Lattice3D ltr = l1.rotated(tr);
// use EXPECT_NEAR as transform (matrix multiplication) uses double value for rotation angle
// e.g. Rotating the vector (1,0,0) by 2*PI about z would give something like (0.99999,0,0)
const double epsilon = 1e-12;
EXPECT_NEAR(a2.x(), ltr.basisVectorA().x(), epsilon);
EXPECT_NEAR(a2.y(), ltr.basisVectorA().y(), epsilon);
EXPECT_NEAR(a2.z(), ltr.basisVectorA().z(), epsilon);
EXPECT_NEAR(-a1.x(), ltr.basisVectorB().x(), epsilon);
EXPECT_NEAR(-a1.y(), ltr.basisVectorB().y(), epsilon);
EXPECT_NEAR(-a1.z(), ltr.basisVectorB().z(), epsilon);
EXPECT_NEAR(a3.x(), ltr.basisVectorC().x(), epsilon);
EXPECT_NEAR(a3.y(), ltr.basisVectorC().y(), epsilon);
EXPECT_NEAR(a3.z(), ltr.basisVectorC().z(), epsilon);
}
// tests the nearest REC. LATTICE point to a given REC. SPACE vector
TEST(Lattice, NearestI3)
{
R3 a1(1, 0, 0);
R3 a2(0, 1, 0);
R3 a3(0, 0, 1);
Lattice3D l1(a1, a2, a3);
// vector_in is in REC. SPACE coordinates
R3 vector_in(2.8 * (2 * pi), 0, 0);
// point_expected is in REC. LATTICE coordinates
I3 point_expected(3, 0, 0);
EXPECT_EQ(point_expected, l1.nearestI3(vector_in));
}
// tests the list of REC. LATTICE vectors (in REC. SPACE coords) computed within a specified
// radius of a given REC. SPACE vector
TEST(Lattice, reciprocalLatticeVectorsWithinRadius)
{
R3 a1(1, 0, 0);
R3 a2(0, 1, 0);
R3 a3(0, 0, 1);
Lattice3D l1(a1, a2, a3);
R3 b1, b2, b3;
l1.reciprocalLatticeBasis(b1, b2, b3);
// vector_in is in REC. SPACE coordinates
R3 vector_in(2.5 * (2 * pi), 0, 0);
// list of REC. LATTICE vectors expected within given radius
std::vector<R3> vectors_expected;
R3 expected_1 = 2 * b1;
R3 expected_2 = 3 * b1;
vectors_expected.push_back(expected_1);
vectors_expected.push_back(expected_2);
EXPECT_EQ(vectors_expected, l1.reciprocalLatticeVectorsWithinRadius(vector_in, (2 * pi)));
EXPECT_EQ(vectors_expected, l1.reciprocalLatticeVectorsWithinRadius(vector_in, (2 * pi) - 0.1));
}
// tests FCC lattice creation
TEST(Lattice, FCCLattice)
{
// creates FCC lattice onto a new Lattice instance l1
Lattice3D l1 = bake::FCCLattice(1);
R3 fcc1(0, 0.5, 0.5);
R3 fcc2(0.5, 0, 0.5);
R3 fcc3(0.5, 0.5, 0);
EXPECT_EQ(fcc1, l1.basisVectorA());
EXPECT_EQ(fcc2, l1.basisVectorB());
EXPECT_EQ(fcc3, l1.basisVectorC());
}
// tests hexagonal lattice creation
TEST(Lattice, HexagonalLattice2D)
{
Lattice3D l1 = bake::HexagonalLattice(1, 4);
R3 tri1(1, 0.0, 0.0);
R3 tri2(-1 / 2.0, std::sqrt(3.0) * 1 / 2.0, 0);
R3 tri3(0.0, 0.0, 4);
EXPECT_EQ(tri1, l1.basisVectorA());
EXPECT_EQ(tri2, l1.basisVectorB());
EXPECT_EQ(tri3, l1.basisVectorC());
}
// tests whether basis and reciprocal vectors are returned correctly when the basis
// vectors are manually changed using the setVectorValue method
TEST(Lattice, onChange)
{
R3 a1(1, 0, 0);
R3 a2(0, 1, 0);
R3 a3(0, 0, 1);
Lattice3D l1(a1, a2, a3);
R3 b1, b2, b3, m_ra, m_rb, m_rc;
// computing expected reciprocal lattice vectors
R3 a23 = a2.cross(a3);
R3 a31 = a3.cross(a1);
R3 a12 = a1.cross(a2);
m_ra = (2 * pi) / a1.dot(a23) * a23;
m_rb = (2 * pi) / a2.dot(a31) * a31;
m_rc = (2 * pi) / a3.dot(a12) * a12;
l1.reciprocalLatticeBasis(b1, b2, b3);
EXPECT_EQ(m_ra, b1);
EXPECT_EQ(m_rb, b2);
EXPECT_EQ(m_rc, b3);
// The new changed lattice vectors
R3 c1(2, 0, 0), c2(0, 2, 0), c3(0, 0, 2);
Lattice3D l2(c1, c2, c3);
EXPECT_EQ(c1, l2.basisVectorA());
EXPECT_EQ(c2, l2.basisVectorB());
EXPECT_EQ(c3, l2.basisVectorC());
R3 d1, d2, d3, mc_ra, mc_rb, mc_rc;
// computing the expected changed reciprocal lattice vectors
R3 c23 = c2.cross(c3);
R3 c31 = c3.cross(c1);
R3 c12 = c1.cross(c2);
mc_ra = (2 * pi) / c1.dot(c23) * c23;
mc_rb = (2 * pi) / c2.dot(c31) * c31;
mc_rc = (2 * pi) / c3.dot(c12) * c12;
l2.reciprocalLatticeBasis(d1, d2, d3);
EXPECT_EQ(mc_ra, d1);
EXPECT_EQ(mc_rb, d2);
EXPECT_EQ(mc_rc, d3);
}
|
